Question

Two identical spheres are placed in contact with each other. If their radii are varied keeping their mass constant, find the relation between gravitational attraction $F$ and radius of the spheres $R$. Assume the radii of both the spheres to be identical at all instances.

• A. $F\propto R^2$
• B. $F\propto R^4$
• C. $F\propto \frac{1}{R^2}$
• D. $F\propto \frac{1}{R^4}$

Answer 1

The correct option is C

$F\propto \frac{1}{R^2}$

The two identical spheres behave as point masses with all the mass concentrated at the centre.
Given radius of each sphere is $R$. Since the two spheres are kept in contact with each other, the distance between their centres is $2R$.

According to the universal law of gravitation, the gravitational force between two bodies is inversely proportional to the square of the distance between them.
$F\propto \frac{1}{4R^2}$
Since '4' is a constant, we can write, $F\propto \frac{1}{R^2}$